Find the minimum distance between the point (-3,2) and the line y = -x + 1
(Enter an exact answer with a square root.)
Answers
The minimum distance between the point(-3,2) and the line y = -x + 1 is [tex]\sqrt{2}[/tex] units.
What is a line segment?The line that joins two points on a cartesian plane is a line segment.
Analysis:
The formula for calculating distance between a line and a point is
d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]
where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.
x1 and y1 are coordinates of the point.
for the line y = -x + 1 which is = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units
In conclusion, the distance between the point and the line is [tex]\sqrt{2}[/tex] units
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Related Questions
In the arithmetic sequence {13, 6,-1,-8,...}, what is the common difference?
Answers
Explanation:
Pick any term. Subtract off the previous one to find the common difference.
term2 - term1 = 6-13 = -7term3 - term2 = -1-6 = -7term4 - term3 = -8-(-1) = -8+1 = -7And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.
We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.
Use the figure.
10 feet
4 feet
10 feet
7 feet
Find the perimeter of the figure.
Answers
Primeter=10 + 4 +10 +7 = 31 ft
I need it done asap please help before 12:00
Answers
The product of three consecutive integers is 30 times the smallest of the three
integers. Find the two possible sets of integers that will satisfy this condition.
Answers
AnswEr :
Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]
⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.
[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]
Therefore ,
When , x = 2 ,
First Integer : x , 2 ,Second Integer : ( x +1 ) , 3 & Third Integer : ( x +2 ) = 4 .When , x = –7 ,
First Integer : x , – 7 ,Second Integer : ( x +1 ) , – 6 & Third Integer : ( x +2 ) = – 5 .Answer:
Hi,
Step-by-step explanation:
If the "is" means is equal to
Let's say a-1, a, a+1 the 3 consecutive integers.
[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]
[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]
The two sets are : (0,1,2) and (4,5,6).
I need this asap plsss help me!!!!!
Answers
If the diameter is d = 8, then we divide that in half to get the radius of r = 4.
If the radius is r = 9, then we double it to get the diameter of d = 18
The formulas are:
radius = diameter/2diameter = 2*radiusI'll let you determine the others.
Answer:
Step-by-step explanation:
Diameter is twice the radius. d = 2*r
Radius is half the diameter r = d÷2
1) d = 8
r = 8÷ 2
r = 4
2) r = 9
d = 2*r
= 2*9
d = 18
3) r = 24
d = 24*2 =48
4) d = 36
r = 36 ÷2 = 18
5) d = 52
r = 52÷2 = 26
What property states that changing the order of two or more terms does what to the value of the sum
Answers
Answer: Commutative property
how many solutions does 9x+5=9x+7
Answers
Answer:
There are 0 solutions to this problem because it cannot be re-arranged logically enough to come to a new conclusion.
Answer:
0
Step-by-step explanation:
If we try to solve this question, we get no solutions:
First we subtract 5 from both sides :
9x = 9x + 2
Now we subtract 9x from both sides :
0 = 0 +2
0 = 2 ❌
This is why this equation has no solutions
Hope this helped and have a good day
Is the graph increasing, decreasing, or constant?
Answers
Answer:
increasing to the certain point
Step-by-step explanation:
Potato head
Distance (km)
a.
b.
c.
d.
400
300
200
100
Travel Rate
(3, 318)
(1, 106)
(0, 0)
1
(2,212)
111 km/h
106 km/h
102 km/h
97 km/h
2 3
Time (h)
Answers
Answer:
good and right and keep trying your best
One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 58 meters
Answers
Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
Equation 1
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
Conclusion
The dimensions of the rectangle are:
width = 7 meterslength = 22 metersTherefore, the length of the longer side is 22 meters
The length of the longer side is 22 meters.
Let, one side of the rectangle is x meters.
According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 58 meters:
58 = 2 * (x + 4x - 6)
Now, let's solve for x:
58 = 2 * (5x - 6)
58 = 10x - 12
Add 12 to both sides:
58 + 12 = 10x
70 = 10x
Now, divide both sides by 10 to isolate x:
x = 70 / 10
x = 7
So, one side of the rectangle is 7 meters.
Now, we can find the length of the longer side:
Length of the longer side = 4x - 6
Length of the longer side = 4 * 7 - 6
Length of the longer side = 28 - 6
Length of the longer side = 22 meters
Therefore, the length of the longer side is 22 meters.
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Max w = 5y1 + 3y2
s. a.
y1 + y2 ≤ 50
2y1 + 3y2 ≤ 60
y1
, y2 ≥ 0
Answers
The maximum value of the objective function is 330
How to maximize the objective function?The given parameters are:
Max w = 5y₁ + 3y₂
Subject to
y₁ + y₂ ≤ 50
2y₁ + 3y₂ ≤ 60
y₁ , y₂ ≥ 0
Start by plotting the graph of the constraints (see attachment)
From the attached graph, we have:
(y₁ , y₂) = (90, -40)
Substitute (y₁ , y₂) = (90, -40) in w = 5y₁ + 3y₂
w = 5 * 90 - 3 * 40
Evaluate
w = 330
Hence, the maximum value of the function is 330
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Sine is opposite divided by hypotenuse. So the sine of an angle times the hypotenuse is the length of the opposite side. What is the length of the side opposite a 30 degree angle for a right triangle with a hypotenuse of 20 meters?
Answers
Answer:
10 m
Step-by-step explanation:
opposite = sin30° × 20 = [tex]\frac{1}{2}[/tex] × 20 = 10 m
CAN SOMEONE PLEASE PLEASE HELP ME?? I’LL GIVE YOU FREE EASY POINTS AND IT’S ONLY 4 QUESTIONS. JUST MAKE SURE YOU GIVE THE RIGHT ANSWERS PLSS. THE PICTURE IS ABOVE IF ANYBODY NEEDS TO SEE IT!
Answers
Answer:
Step-by-step explanation:
1. To find f(0.5), substitute the x value in the function f(x) with 0.5
f(x) = 30x + 5
f(0.5) = 30*0.5 + 5
= 15 + 5
= 20
At 0.5 gigabytes of data used, the cost is $20
2) g(x) = 10x + 20
g(0.5) = 10*0.5 + 20
= 5 + 20
= 25
At 0.5 gigabytes of data used, the cost is $ 25.
3) f(x) = 50
30x + 5 = 50
Subtract 5 from both sides
30x = 50 - 5
30x = 45
Divide both sides by 30
x = 45/30
x = 1.5
If she chooses plan 'f', she could use 1.5 gigabytes.
g(x) = 50
10x + 20 = 50
10x =50- 20
10x = 30
x = 30/10
x = 3
If she chooses plan 'g', she could use 3 gigabytes.
4) Function 'g' would be better for a $50 monthly budget as she could get more gigabytes than function 'f'
Find the present value, using the future value formula and a calculator. Future value is $6,000 in two years at 9.5% simple interest. Round your answer to the nearest cent (two decimal places). Enter only the number without $ sign.
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6000\\ P=\textit{original amount deposited}\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=years\dotfill &2 \end{cases} \\\\\\ 6000=P[1+(0.095)(2)]\implies \cfrac{6000}{1.19}=P\implies 5042.02\approx P[/tex]
if f(x)=2x-1 and g(x)=x^2-4, what is g(f(x))
Answers
Answer:
4x^2 - 4x - 3
Step-by-step explanation:
f(x) = 2x - 1
g(x) = x^2 - 4
g(f(x)) = ?
[substitute the x of g(x) with f(x)]
g(x) = x^2 - 4
g(f(x)) = (2x - 1)^2 - 4
[solve]
[binomial * binomial = quadratic equation]
[use FOIL method (first, outer, inner, last)]
g(f(x)) = (2x - 1)(2x - 1) - 4
g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4
[combine like terms]
g(f(x)) = 4x^2 - 2x - 2x + 1 - 4
g(f(x)) = 4x^2 - 4x - 3
Work out the coordinate of R
Answers
Answer:
The problem is with the arrangement of the ratios
PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR
Answer:
[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]
Step-by-step explanation:
Coordinates of the extreme points of the segment are P(-4, -1) and Q (6, 11)[tex]\implies x_1= -4,\:y_1=-1,\:x_2=6,\:y_2=11[/tex]PQ = 4PR (Given)......(1)PQ = PR + RQ.....(2)-> 4PR = PR + RQ [From (1) and (2)]-> 4PR - PR = RQ-> 3PR = RQ-> PR/RQ = 1/3-> PR : RQ = 1 : 3This means point R divides segment PQ in the ratio 1 : 3.-> m : n = 1 : 3Now, coordinates of point R can be obtained by the section formula for internal division, which is given below:[tex]R=\bigg(\frac{mx_2+nx_1}{m+n},\:\frac{my_2+ny_1}{m+n}\bigg)[/tex][tex]\implies R=\bigg(\frac{1(6)+3(-4)}{1+3},\:\frac{1(11)+3(-1)}{1+3}\bigg)[/tex][tex]\implies R=\bigg(\frac{6-12}{4},\:\frac{11-3}{4}\bigg)[/tex][tex]\implies R=\bigg(\frac{-6}{4},\:\frac{8}{4}\bigg)[/tex][tex]\implies\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]Place the indicated product in the proper location on the grid. (4a + x)(a-x)
Answers
Step-by-step explanation:
4a(a-x)+x(a-x)
[4a]2-4ax+ax-(x)2
(4a)2-3ax-(x)2
Five times the sum of a number and -23.
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We need to translate "five times the sum of a number and -23" into an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Can you see the word "sum" there? It tells us to add.So in this case we should add a number (let it be x) and -23:
[tex]\star~\large\pmb{x+-23}[/tex]
Which is the same thing as
[tex]\star~\large\pmb{x-23}[/tex]
Now we multiply this little expression by 5, which gives us
[tex]\star~\large\pmb{5(x-23)}[/tex]
The parentheses around the expression indicate that we multiply 5 by the entire expression, and not just one term.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
During the basketball season, Morgan made 3 times as many 2-point baskets as she made 3-point baskets and free throws combined. If she made 14 free throws and eight 3-point baskets, How many 2-point baskets did she make. And simplify your answer.
Answers
Answer:
123 save some for me
Step-by-step explanation:
:0
Answer: 123
Step-by-step explanation: I did the math- lol-
D = {f, g, k}
L = {a,f,j}
Find the intersection of D and L.
Find the union of D and I.
Answers
Answer:
Step-by-step explanation:
D∩L={f}
D∪L={a,f,g,j,k}
The line segment located in the circle below is the circle’s ____________
Pi
Area
Radius
Diameter
Circumference
Answers
Find the missing angle
120 & 30
y = [???]
Answers
Answer:
z = 30
Step-by-step explanation:
All angles of a triangle add up to 180:
z + 120 + 30 = 180
z + 150 = 180
z = 180 - 150
z = 30
Which of these steps will eliminate a variable in this system?
4x - 9y = 8
2x + 3y = 24
A. Multiply the first equation by 3. Then subtract the second equation from the first.
B. Multiply the second equation by 2. Then add the equations.
C. Multiply the second equation by 2. Then subtract the second equation from the first.
D. Multiply the second equation by 3. Then subtract the second equation from the first.
Answers
Answer:
option c is correctStep-by-step explanation:
for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:
FOR OPTION A
if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.
FOR OPTION B
if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x
FOR OPTION C if the second equation is multiplied by 2, our new equation 2 becomes 4x + 6y= 48 and if we subtract, 4X-4x= 0 so we have eliminated X ( option C is correct)FOR OPTION D
if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y
how many different sample size of n=3 can be drawn from the population
Answers
I'll focus on question 10 only. Let me know if you need me to answer the others.
We have the population with this set of numbers: {2,4,6,8,10}
There are 5 values in that set.
Now consider having slots labeled A,B and C to represent the three placeholders for the numbers.
For slot A, we have 5 choicesSlot B has 5-1 = 4 choicesSlot C has 5-2 = 3 choicesThere are 5*4*3 = 20*3 = 60 permutations and 60/(3*2*1) = 60/6 = 10 combinations.
Therefore, we have 10 different subsamples of 3 items.
Answer: Choice C) 10Which best tells how heavy a dog might be?
A dog is shown.
A.
100 g
B.
25 kg
C.
25 g
D.
100 kg
Answers
Answer:
B
Step-by-step explanation:
A dog might be around
b) 25 kgs
Evaluate the expression shown below and write your answer as a fraction in simplest form. 16/11 − 12/1
Answers
Answer:
-10 6/11
Step-by-step explanation:
16/11−12/1=16/11+−12/1=16/11+−132/11=16+−132/11=−116/11
-116/11 = −10 6/11
The drama club meets in the school auditorium every 8 days, and the choir meets there every 6 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?
Answers
You need to find the least common multiple of 8 and 6.
[tex]8=2^3\\6=2\cdot3\\\\\text{lcm}(8,6)=2^3\cdot3=24[/tex]
Therefore, the answer is 24 days.
Find the domain and range of the function:
--√√5-x-3
Answers
The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]
How to determine the domain and the range?The function is given as:
[tex]f(x) = \sqrt{5 - x} - 3[/tex]
The radicand must be at least 0.
So, we have:
[tex]\sqrt{5 - x} \ge 0[/tex]
Square both sides
[tex]5 - x \ge 0[/tex]
Rewrite as:
[tex]5 \ge x[/tex]
Solve for x
[tex]x \le 5[/tex]
This means that the domain is [tex]x \le 5[/tex]
For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]
This means that:
[tex]f(x) \ge 0 - 3[/tex]
[tex]f(x) \ge - 3[/tex]
Hence, the range of the function is [tex]f(x) \ge - 3[/tex]
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Solve this for me please
Answers
Answer:
a=11,b=7 Is the correct answer
Please mark me as brainliest
Answer:
a = 11 and b = 7
Step-by-step explanation:
Multiply numerical values 5 x (-4) then add exponents of like terms x⁷(x⁴) = x¹¹ then y²(y⁵) = y⁷
Ryan is on a game show. He will choose a box to see if he wins a prize. The odds in favor of Ryan winning a prize are 5/7.
Find the probability of Ryan winning a prize.
Answers
The probability of Ryan winning a prize would be 0.71.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Ryan is on a game show. He will choose a box to see if he wins a prize.
The odds in favor of Ryan winning a prize are 5/7.
P(Ryan wins a prize) = 5/7 = 0.71
Thus, the probability of Ryan winning a prize would be 0.71.
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